Article ID Journal Published Year Pages File Type
8904452 Acta Mathematica Scientia 2017 22 Pages PDF
Abstract
In this paper we study a fractional stochastic heat equation on Rd(d≥1) with additive noise ∂∂tu(t,x)=dδ_α_u(t,x)+b(u(t,x))+W˙H(t,x) where dδ_α_ is a nonlocal fractional differential operator and W˙H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d=1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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